IDEAS home Printed from
   My bibliography  Save this article

Likelihood-Based EWMA Charts for Monitoring Poisson Count Data With Time-Varying Sample Sizes


  • Qin Zhou
  • Changliang Zou
  • Zhaojun Wang
  • Wei Jiang


Many applications involve monitoring incidence rates of the Poisson distribution when the sample size varies over time. Recently, a couple of cumulative sum and exponentially weighted moving average (EWMA) control charts have been proposed to tackle this problem by taking the varying sample size into consideration. However, we argue that some of these charts, which perform quite well in terms of average run length (ARL), may not be appealing in practice because they have rather unsatisfactory run length distributions. With some charts, the specified in-control (IC) ARL is attained with elevated probabilities of very short and very long runs, as compared with a geometric distribution. This is reflected in a larger run length standard deviation than that of a geometric distribution and an elevated probability of false alarms with short runs, which, in turn, hurt an operator's confidence in valid alarms. Furthermore, with many charts, the IC ARL exhibits considerable variations with different patterns of sample sizes. Under the framework of weighted likelihood ratio test, this article suggests a new EWMA control chart which automatically integrates the varying sample sizes with the EWMA scheme. It is fast to compute, easy to construct, and quite efficient in detecting changes of Poisson rates. Two important features of the proposed method are that the IC run length distribution is similar to that of a geometric distribution and the IC ARL is robust to various patterns of sample size variation. Our simulation results show that the proposed chart is generally more effective and robust compared with existing EWMA charts. A health surveillance example based on mortality data from New Mexico is used to illustrate the implementation of the proposed method. This article has online supplementary materials.

Suggested Citation

  • Qin Zhou & Changliang Zou & Zhaojun Wang & Wei Jiang, 2012. "Likelihood-Based EWMA Charts for Monitoring Poisson Count Data With Time-Varying Sample Sizes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1049-1062, September.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:499:p:1049-1062 DOI: 10.1080/01621459.2012.682811

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. Hilary W. Hoynes & Diane Whitmore Schanzenbach, 2009. "Consumption Responses to In-Kind Transfers: Evidence from the Introduction of the Food Stamp Program," American Economic Journal: Applied Economics, American Economic Association, vol. 1(4), pages 109-139, October.
    2. Charles F. Manski, 1997. "Monotone Treatment Response," Econometrica, Econometric Society, vol. 65(6), pages 1311-1334, November.
    3. Nord, Mark & Andrews, Margaret S. & Carlson, Steven, 2008. "Household Food Security in the United States, 2007," Economic Research Report 56483, United States Department of Agriculture, Economic Research Service.
    4. Moffitt, Robert, 1983. "An Economic Model of Welfare Stigma," American Economic Review, American Economic Association, vol. 73(5), pages 1023-1035, December.
    5. Brent Kreider & John Pepper, 2008. "Inferring disability status from corrupt data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(3), pages 329-349.
    6. Kreider, Brent & Pepper, John V., 2007. "Disability and Employment: Reevaluating the Evidence in Light of Reporting Errors," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 432-441, June.
    7. Craig Gundersen & Victor Oliveira, 2001. "The Food Stamp Program and Food Insufficiency," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 83(4), pages 875-887.
    8. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    9. Kaushal, N., 2007. "Do food stamps cause obesity?: Evidence from immigrant experience," Journal of Health Economics, Elsevier, vol. 26(5), pages 968-991, September.
    10. Bollinger, Christopher R., 1996. "Bounding mean regressions when a binary regressor is mismeasured," Journal of Econometrics, Elsevier, vol. 73(2), pages 387-399, August.
    11. Charles F. Manski & John V. Pepper, 2000. "Monotone Instrumental Variables, with an Application to the Returns to Schooling," Econometrica, Econometric Society, vol. 68(4), pages 997-1012, July.
    12. John V. Pepper, 2000. "The Intergenerational Transmission Of Welfare Receipt: A Nonparametric Bounds Analysis," The Review of Economics and Statistics, MIT Press, vol. 82(3), pages 472-488, August.
    13. Brent Kreider & Steven C. Hill, 2009. "Partially Identifying Treatment Effects with an Application to Covering the Uninsured," Journal of Human Resources, University of Wisconsin Press, vol. 44(2).
    14. Bhattacharya, Jayanta & Currie, Janet & Haider, Steven, 2004. "Poverty, food insecurity, and nutritional outcomes in children and adults," Journal of Health Economics, Elsevier, vol. 23(4), pages 839-862, July.
    15. Craig Gundersen & Susan Offutt, 2005. "Farm Poverty and Safety Nets," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 87(4), pages 885-899.
    16. Anne Case & Darren Lubotsky & Christina Paxson, 2002. "Economic Status and Health in Childhood: The Origins of the Gradient," American Economic Review, American Economic Association, vol. 92(5), pages 1308-1334, December.
    17. Chad D. Meyerhoefer & Yuriy Pylypchuk, 2008. "Does Participation in the Food Stamp Program Increase the Prevalence of Obesity and Health Care Spending?," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 90(2), pages 287-305.
    18. Molinari, Francesca, 2010. "Missing Treatments," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 82-95.
    19. Janet Currie, 2003. "U.S. Food and Nutrition Programs," NBER Chapters,in: Means-Tested Transfer Programs in the United States, pages 199-290 National Bureau of Economic Research, Inc.
    Full references (including those not matched with items on IDEAS)

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:jnlasa:v:107:y:2012:i:499:p:1049-1062. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Chris Longhurst). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.